What's your OS? I know Windows 10 has an audio bug when certain USB peripherals are active where you need to disable and then enable an audio device for certain applications to recognize them. It's worth a shot if you've exhausted all other options.
Start pCars
Alt out, go into Windows audio device settings, click disable check box and then re-enable it again - and see if it shows up in pCars again. Might have to restart.
A bit tedious, but it's simply a diagnostic process until we can go further.
Good luck